1 | U n i t 6 10P Date:___________ Name: _______________________

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DAY 1 - Pythagorean Theorem

1. 2.

3.

2 | U n i t 6 10P Date:___________ Name: _______________________

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4. 5.

6. 7.

3 | U n i t 6 10P Date:___________ Name: _______________________

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IF there’s time Investigation:

Complete the table below using the triangles provided. Round answers to one decimal place.

Triangle opposite

hypotenuse sin A

adjacent

hypotenuse cos A

opposite

adjacent tan A

∆∆∆∆ABC

∆∆∆∆XYZ

1. What do you notice about the ratios of lengths of sides and the trigonometric ratios in both triangles?

2. Ways to label triangle angles and sides. Small case vs capitals, inside triangle vs outside, where angles and

sides go in equations, how to round

C

B

A 4 cm

5 cm

3 cm

37°

Z

Y

X 12 cm

15 cm

9 cm

37°

4 | U n i t 6 10P Date:___________ Name: _______________________

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DAY 2 - Primary Trig Ratios – SOH CAH TOA – solving for sides

1. Practice labelling tiangles using side names: opposite, adjacent, hypotenuse.

MAKE SURE your calculator is in DEGREE mode! 2. Use a scientific calculator to find each value to four decimal places. a) sin 65° b) sin 48° c) cos 35° d) cos 58° e) tan75° f) tan39°

3. Solve for side x

a.

b.

c.

X

14 m

29o

75 cm

X 26o

8 m

X

21o

5 | U n i t 6 10P Date:___________ Name: _______________________

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4. 5.

6. 7.

6 | U n i t 6 10P Date:___________ Name: _______________________

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DAY 3 - More Practice SOH CAH TOA 1.

MAKE SURE your calculator is in DEGREE mode!

2. Use a scientific calculator to find the measure of each ∠ to the nearest degree.

a) sin A = 0.8192 b) sin A = 0.9962 c) tan B = 0.9063 d) cos B = -0.8480 e) cos B = 0.1233 f) tan B = 0.6680

3. Solve for angle ϴ

a.

b.

c.

θ°

2 cm

4 cm

θ °

12 cm

8 cm

θ ° 13 cm

6 cm

7 | U n i t 6 10P Date:___________ Name: _______________________

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4. Solve the following for x.

a.

b.

c.

d.

5. 6.

X 24 cm

32 cm 49o

36 m

x

X

21 cm

16 cm

11 m

X

51o

8 | U n i t 6 10P Date:___________ Name: _______________________

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DAY 4 - Similar Triangles

1. Write a proportionality statement for each pair of similar triangles

2. For each pair of similar triangles find the missing measures

9 | U n i t 6 10P Date:___________ Name: _______________________

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3. For each pair of similar triangles find the measure asked

4. 5.

A person 1.9 m tall casts a shadow 3.8 m long. At the same time a tree casts a shadow 18 m long. Find the height of the tree.

6. 7.

10 | U n i t 6 10P Date:___________ Name: _______________________

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DAY 5 – More Similar Triangles

Are the triangles similar? If so, write a similarity statement and the ratio proportion statement

11 | U n i t 6 10P Date:___________ Name: _______________________

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7. Find the unknown angle if ABC DEF∆ ≈ ∆

8. Find the unknown sides

a. b.

9. The tips of the shadows of a flagpole and a 1.5-m

fence post meet at the point S. The following

lengths are measured: ST = 2.7 m and QT = 7.4 m.

Use this information to find the height of the

flagpole. Round your answer to the nearest tenth

of a metre.

10.

12 | U n i t 6 10P Date:___________ Name: _______________________

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DAY 6 - Solve Word Problems

1. 2.

A wheelchair ramp is 2.5 m. The horizontal distance from the end of the ramp to the building is 2 m. What angle does the ramp make with the ground?

Sheryl’s tree house is 3 m above the ground. Sheryl looks down at an angle of depression of 30° and can see her poodle’s doghouse. What is the horizontal distance from the doghouse to the tree house?

3. 4.

Ralph is on the roof of a building, while his friend Ajay is on the ground. Ralph can see Ajay at a 50° angle of depression. The vertical height of the building is 20 m. What is the diagonal distance from Ralph to where Ajay is standing?

From a point 6.5 m from the base of the school flagpole, the angle of elevation to the top of the flagpole is 46°. What is the height of the flagpole?

5. 6.

13 | U n i t 6 10P Date:___________ Name: _______________________

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7. 8.

The angle of depression from the top of a castle to a boat is

25°. If the distance from the top of the castle to the boat is

determined to be 100 m, how high is the castle?

9. 10.

11. 12.

14 | U n i t 6 10P Date:___________ Name: _______________________

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Practice TEST

1. tan 47° is 2. cos 55° is 3. sin 49° is

4. If sin A = 0.8829, then ∠A is approximately

5. If cos A = 0.8290, then ∠A is approximately 6. A slide in a park has a vertical height of 1.5 m. The

horizontal distance covered by the slide is 2 m. The length of the slide is

7. A cat lying on the ground is 1.5 m away from his

owner. The angle of elevation from the cat to his owner's head is 48°. How tall is his owner?

8. Thi’s model boat has a base 60 cm long. The

horizontal length of the sail is half the length of the

base of the boat. ∠C is 45°. What is the diagonal side of the sail?

9. From a point 9.8 m from the base of a flagpole, the

angle of elevation to the top of the pole is 48°. What is the height of the flagpole?

10. Jan’s tree house is 4.8 m above the ground. When

he looks down at an angle of depression of 40°, he can see over the fence and into his neighbour's backyard. What is the diagonal distance from tree house to the neighbour’s backyard?

15 | U n i t 6 10P Date:___________ Name: _______________________

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11. In �JKL below, JK is 4 cm, JL is 16 cm, and KL is

16.49 cm. a) Write the 3 trig ratios for angle L b) Find angle L

12. In �GHI below, GI is 3.5 m and GH is 3m.

Determine the angle ∠G to the nearest degree.

13. Line segments AC and DE are parallel. Find the

length of AC to the nearest tenth of a unit.

14. Beatriz lives on Arc Avenue, which is 200 m long.

Her aunt's house is on Tumble Street, which is 150 m long.

a) Determine the distance that Beatriz travels if she

goes along both streets from her house to her aunt's house.

b) What is the distance that Beatriz travels if she takes

a diagonal shortcut? c) How much shorter is the shortcut?

15. The height of Melvin’s house is 12 m. His

friend, Matt, lives in a house that is 15 m tall. If

Matt’s house casts a shadow that is 16 m long,

what is the length of the shadow cast by

Melvin’s house to the nearest tenth of a metre?